This paper shows the importance of correcting for sample selection when investing in illiquid assets with endogenous trading. Using a large sample of 20,538 paintings that were sold repeatedly at auction between 1972 and 2010, we find that paintings with higher price appreciation are more likely to trade. This strongly biases estimates of returns. The selection-corrected average annual index return is 6.5 percent, down from 10 percent for traditional uncorrected repeat sales regressions, and Sharpe Ratios drop from 0.24 to 0.04. From a pure financial perspective, passive index investing in paintings is not a viable investment strategy once selection bias is accounted for. Our results have important implications for other illiquid asset classes that trade endogenously.